Patch-PODiff-ViT defines a structured latent space via patchwise POD for efficient diffusion-based super-resolution and direct analytic uncertainty quantification across scientific and natural images.
The proper orthogonal decomposition in the analysis of turbulent flows.Annual review of fluid mechanics, 25(1):539–575
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A differentiable programming framework tunes POD-Galerkin tensors using a hybrid trajectory-plus-energy-conservation loss to stabilize chaotic flow ROMs, achieving accuracy and stability with 20 modes on a Re=30,000 lid-driven cavity where classical methods need 80.
Courant is a state-adaptive Perceiver encoder-processor-decoder surrogate trained with L2 loss that yields interpretable, multiscale, locally supported latent features acting as time-evolving spatial basis functions.
Higher-order LaSDI uses a high-order finite-difference scheme and rollout loss to improve long-term prediction accuracy in reduced-order models for parameterized PDEs, shown on the 2D Burgers equation.
citing papers explorer
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Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification
Patch-PODiff-ViT defines a structured latent space via patchwise POD for efficient diffusion-based super-resolution and direct analytic uncertainty quantification across scientific and natural images.
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A Differentiable Programming Framework for Accurate and Stable Reduced-Order Modeling of Chaotic Flows
A differentiable programming framework tunes POD-Galerkin tensors using a hybrid trajectory-plus-energy-conservation loss to stabilize chaotic flow ROMs, achieving accuracy and stability with 20 modes on a Re=30,000 lid-driven cavity where classical methods need 80.
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Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition
Courant is a state-adaptive Perceiver encoder-processor-decoder surrogate trained with L2 loss that yields interpretable, multiscale, locally supported latent features acting as time-evolving spatial basis functions.
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Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives
Higher-order LaSDI uses a high-order finite-difference scheme and rollout loss to improve long-term prediction accuracy in reduced-order models for parameterized PDEs, shown on the 2D Burgers equation.